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Abstract <p> The paper introduces a new class of field equations (in Minkowski space), which are calledconservative equations. The distinctive features of the introduced equations are their symmetrywith respect to transformations with the unitary group <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10625_2025_2818_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathrm {U}(2)\)</EquationSource> </InlineEquation> and the presence of additional conservation lawscorresponding to the group <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10625_2025_2818_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathrm {U}(2)\)</EquationSource> </InlineEquation>.A gauge invariant system of equations combining the conservative equation and the Yang–Millsequations is considered. It is proposed to use this system of equations to describe the dynamics ofa neutrino with a nonzero mass interacting with the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10625_2025_2818_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathrm {SU}(2)\)</EquationSource> </InlineEquation> Yang–Mills field (weak interaction field).</p>

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Conservative Equations in Field Theory: Conservation and Symmetry Laws

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • N. G. Marchuk

摘要

Abstract

The paper introduces a new class of field equations (in Minkowski space), which are calledconservative equations. The distinctive features of the introduced equations are their symmetrywith respect to transformations with the unitary group \(\mathrm {U}(2)\) and the presence of additional conservation lawscorresponding to the group \(\mathrm {U}(2)\) .A gauge invariant system of equations combining the conservative equation and the Yang–Millsequations is considered. It is proposed to use this system of equations to describe the dynamics ofa neutrino with a nonzero mass interacting with the \(\mathrm {SU}(2)\) Yang–Mills field (weak interaction field).